The three-time Grand Slam champion took just over two-and-a-half hours to seal a three-set triumph on the hard court.
Murray can end the week as world number one if he wins the trophy and Novak Djokovic fails to make the final in the French capital.
"It was a tough match. Verdasco was going for his shots and serving huge," BBC Sport quotes Murray as saying.
"When he was behind in games and even when I was getting the return back, he was dictating the points on his forehand and backhand. He hit a few lines with his backhand. I just had to fight at the end."